Multiply the following complex numbers: $({3+5i}) \cdot ({1+5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3+5i}) \cdot ({1+5i}) = $ $ ({3} \cdot {1}) + ({3} \cdot {5}i) + ({5}i \cdot {1}) + ({5}i \cdot {5}i) $ Then simplify the terms: $ (3) + (15i) + (5i) + (25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (15 + 5)i + 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 3 + (15 + 5)i - 25 $ The result is simplified: $ (3 - 25) + (20i) = -22+20i $